The series converges to tan x for -/2 a. Find the first five terms of the series

Question:

The series

converges to tan x for -π/2

a. Find the first five terms of the series for ln |sec x|. For what values of x should the series converge?

b. Find the first five terms of the series for sec² x. For what values of x should this series converge?

c. Check your result in part (b) by squaring the series given for sec x in Exercise 58.

Data from in Exercise 58

The series

converges to sec x for -π/2

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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Question Posted: May 05, 2023 07:20 AM

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The series converges to tan x for -/2 a. Find the first five terms of the series

Question:

tan x = x + 17x7 2x5 + 3 15 315 + + 62x⁹ + 2835

Step by Step Answer:

a We know that ln sec x ln 1cos x ln cos x Using the Taylor series for ln1 y we have ln cos x ln 1 t...View the full answer

Thomas Calculus Early Transcendentals

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